Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8×C13 · Schur multiplier (H2) = C24×C8 |
| direct product | C2×C13×#1450 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8×C13 | C22 |
| commutator | C2 | C22×C4×C8×C13 |
| Frattini, cosocle | C42 | C24×C13 |
| socle | C23×C13 | C2×C42 |
| prime radical | C24×C13 | C42 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8×C13 ◁ G | |
982 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39);(11,12,14,17,15,18,21,24)(13,16,20,23,19,22,25,26);(3,4,5,7,6,8,9,10)(11,13)(12,16)(14,20)(15,19)(17,23)(18,22)(21,25)(24,26);(13,19)(16,22)(20,25)(23,26)2080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 10301);